Nonlinear dynamics of feedback modulated magnetic islands in toroidal plasmas

An analysis is presented of the dynamics of a helical magnetic island chain embedded in a toroidal plasma, in the presence of an externally imposed, r otating, magnetic perturbation of the same helicity. Calculations are carri ed out in the large aspect-ratio, zero-p, resistive magnetohydrodynamical l imit, and incorporate a realistic treatment of plasma viscosity. There are three regimes of operation, depending on the modulation frequency (i.e., th e difference in rotation frequency between the island chain and the externa l perturbation). For slowly modulated islands, the perturbed velocity profi le extends across the whole plasma. For strongly modulated islands, the per turbed velocity profile is localized around the island chain, but remains m uch wider than the chain. Finally, for very strongly modulated islands, the perturbed velocity profile collapses to a boundary layer on the island sep aratrix, plus a residual profile which extends a few island widths beyond t he separatrix. Analytic expressions are obtained for the perturbed velocity profile, the island equation of motion, and the island width evolution equ ation in each of these thrice regimes. The ion polarization correction to t he island width evolution equation, which has previously been reported to b e stabilizing, is found to be destabilizing in all three regimes. (C) 2000 American Institute of Physics. [S1070-664X(00)01512-3].